A spring system with 2 DOF

Figure 1 A spring model

A spring model shown in Figure 1 is a system with two DOF, and the system has two masses, joints and spring entities. Their material properties, spring and damping coefficients are shown in Table 1.

Table 1  Material properties, spring and damping coefficients

If the rotational angle  is small,  and the equation of motion of the system can be derived as:

                     (1)

Substituting the values in Table 1, Eq. (1) becomes

                            (2)

The analytic natural frequencies of Eq. 2 are

               (3)

The eigenvalues of this spring system are validated in Table 2.

Table 2  Eigenvalues of spring model